NCEE0
NATIONAL CENTER FOR
ENVIRONMENTAL ECONOMICS
Optimal Border Policies for Invasive Species under
Asymmetric Information
Linda Fernandez and Glenn Sheriff
Working Paper Series
Working Paper # 10-03
March, 2010
stA}.^ U.S. Environmental Protection Agency
National Center for Environmental Economics
1200 Pennsylvania Avenue, NW(MC 1809)
JQL ,
|^L $ Washington, DC 20460
K. S? http://www.epa.gov/economics
i *
o
\
-------
Optimal Border Policies for Invasive Species under
Asymmetric Information
Linda Fernandez and Glenn Sheriff
NCEE Working Paper Series
Working Paper # 10-03
March, 2010
DISCLAIMER
The views expressed in this paper are those of the author(s) and do not necessarily represent
those of the U.S. Environmental Protection Agency. In addition, although the research described
in this paper may have been funded entirely or in part by the U.S. Environmental Protection
Agency, it has not been subjected to the Agency's required peer and policy review. No official
Agency endorsement should be inferred.
-------
Optimal
border policies for invasive species under
information*
asymmetric
Linda Fernandez"'" and Glenn Sheriff*
March 26, 2010
Abstract
This paper analyzes border protection policies for managing risk of unintended imports of invasive
species. Previous work typically assumes invasive species risk to be exogenous and commonly known.
Here, we examine cases in which endogenous actions (exporter abatement) affect risk and allow for
unobservable differences in exporter abatement cost. We show how the optimal inspection/penalty
regime differs in such cases from that derived for homogeneous exporters. The information asymme-
try also makes it optimal for the regulator to provide technical assistance grants even if it would be
otherwise inefficient to do so. Further, we show that the fungibility of technical assistance with inputs
in other sectors of the exporting economy significantly affects the qualitative nature of the optimal
policy. If it has no outside value in the exporter's country, the optimal policy is characterized by a
menu of contracts trading off higher tariffs with lower penalties for being caught with an invasive.
If technical assistance can be used in other sectors of the exporter's economy, it introduces counter-
vailing incentives that make it optimal for the regulator to use a uniform tariff/penalty combination
for all exporters.
Key words: Asymmetric Information, Inspection, International Trade, Invasive Species,
Subject Area Classification: 18, 47
*The authors gratefully acknowledge helpful comments from Peyton Ferrier, Duncan Knowler, Frank Lupi, and
David Simpson. Funding was provided by a grant from the Program of Research on the Economics of Invasive Species
Management administered by the Economic Research Service of the U.S. Department of Agriculture. The views
expressed in this paper do not necessarily represent those of the U.S. Environmental Protection Agency.
^University of California Riverside, Department of Environmental Sciences, linda.f ernandezOucr. edu.
* Corresponding author. U.S. Environmental Protection Agency, National Center for Environmental Economics,
1200 Pennsylvania Ave. (1809T) NW, Washington, DC 20015, 202-566-2265 sheriff.glenn@epa.gov.
1
-------
Introducing non-native flora and fauna can potentially cause severe disruptions in both domestic
ecosystems and domestic economic production. Although some invasive species are deliberately im-
ported (such as for horticultural purposes), many are unintended passengers on other traded goods
or their packaging. Recognizing this threat, many countries have introduced phytosanitary border
control measures comprising random inspections, penalties (e.g., requirements that cargo infected
with invasive species be fumigated or destroyed), as well as alternative approaches such as providing
training or other forms of technical assistance to help exporters reduce the threat of infection before
the good arrives. Departing from earlier literature, we analyze the optimal mix of such instruments,
paying particular attention to cases where there is asymmetric information. Due to local conditions
affecting pest populations, for example, the exporter may be better informed than the regulator
regarding both the cost of abating invasive risk and the amount of abatement undertaken.
There are two broad categories of policy instruments for managing invasive species, those focused
on controlling populations after arrival, and those focused on preventing arrival. One branch of the
economics literature addressing invasive species (e.g., Shogren, 2000; Olson and Roy, 2005; Kim
et al., 2006; Burnett et al., 2008) uses bio-economic modeling to analyze the optimal mix of generic
control and prevention strategies. Another branch (e.g., Eiswerth and Johnson, 2002; Olson and
Roy, 2002; Buhle et al., 2005) exclusively examines control strategies for established invasives.
A third branch, to which this paper belongs, analyzes relative merits of specific border control
mechanisms such as import tariffs (e.g., Costello and McCausland, 2003; Batabyal and Beladi, 2009),
risk abatement subsidies (e.g., Horan and Lupi, 2005), and random inspections and possible penalties
(e.g., McAusland and Costello, 2004; Merel and Carter, 2008). Costello and McCausland (2003) show
that purely protectionist measures (such as import tariffs) may reduce damages from invasives, but
can also potentially increase expected damages by increasing the size of the vulnerable import-
competing sector. In a two country model, Batabyal and Beladi (2009) show that the optimal import
tariff taking into account invasive damages can vary depending upon market structure (e.g., country
size or monopoly power).
Although tariffs can potentially reduce risk by restricting trade, they are blunt instruments and
do not give exporters an incentive to undertake risk abating activity. Horan and Lupi (2005) consider
the problem of inducing exporters to undertake such measures. In a simulation of ballast water-borne
invasive species in the Great Lakes, they compare the cost reduction of a performance-proxy based
subsidy (which allows exporters flexibility in their choice of action) relative to a subsidy linked to a
particular technology. These importer-provided subsidies are analogous to the technical assistance
instrument used in our analysis.
2
-------
McAusland and Costello (2004) and Merel and Carter (2008) are the two papers most closely
related to our model. McAusland and Costello (2004) develop a model of a regulator tasked with
choosing tariffs and inspection intensity to maximize domestic consumer surplus and tax revenue,
less expected damages from invasives. Implicitly, an exporter's penalty for being discovered with an
invasive is destruction of the shipment. Merel and Carter (2008) extend this model, analyzing an
optimal penalty with endogenous exporter response.
Our model extends McAusland and Costello (2004) and Merel and Carter (2008) to character-
ize fully an optimal policy if the regulator cannot observe exporter heterogeneity.1 Costello et al.
(2007) provide evidence that invasive risk varies by trading partner. Information on an exporter's
idiosyncratic risk may be asymmetric if, for example, the invasive species is an insect pest. Pest pop-
ulations can vary both across time and space with current local environmental conditions leading to
risk-reduction costs that vary by producer. As a result, they may undertake different levels of effort
and thus have better knowledge about the ultimate riskiness of their cargo than the regulator.
Our work in this area is also related to the food safety literature (e.g., Starbird, 2005; Gramig
et al., 2009; Sheriff and Osgood, 2010). Starbird (2005) addresses optimal monitoring and penal-
ties with endogenous risk abatement taken by homogenous producers. Sheriff and Osgood (2010)
examine optimal testing for livestock disease when exposure is privately known by heterogeneous
producers, but risk abatement is not possible. Gramig et al. (2009) assume that producers are ex
ante homogenous, but product quality is heterogeneous after endogenous risk abatement takes place.
Our model differs from these earlier approaches both in the array of instruments at the regulator's
disposal (in particular the inspection intensity and technical assistance) as well as their assumption
that producers know their own product quality as well as their abatement action (in our model
exporters know costs and actions, but not the ultimate status of their cargo).
In addition to considering information asymmetry, we extend the model to include the additional
policy option of technical assistance. Importing countries often undertake technical assistance to
prevent or minimize domestic harm from invasives. Since 1967, for example, the North American
Plant Protection Organization (NAPPO), has led both regional (Canada, Mexico, and United States)
and international efforts to harmonize protection of agricultural, forest and other plant resources
against regulated pests while facilitating trade. NAPPO has sponsored technical assistance and pre-
clearance to prevent the introduction and spread of regulated pests as a cost-effective alternative
to eradication.2 NAPPO has funded Canadian experts to provide technical assistance for Peru,
1 McAusland and Costello (2004) briefly discuss an example in which differences in exporter characteristics may
lead to a suboptimal outcome without formally solving the regulator's problem.
2Eradication efforts have had only limited success once an invasive species becomes established.
3
-------
Argentina, China, Korea, Russia, Malaysia and others to help them meet international standards
for treatment of wood-packaging material to kill wood-boring insects (International Standards for
Packaging Material [ISPM] #15). Another example of technical assistance involves Dracaena, an
ornamental plant that can carry invasive grasshoppers, cycadelits, scales, and snails. U.S. Animal
and Plant Health Inspection Service specialists from the Port of Miami have been providing training
to Costa Rican exporters for development of a Clean Stock program to reduce invasive risk at each
stage of the production and export process.
In our model, technical assistance can be thought of as a payment-in-kind of abatement effort. We
consider two classes of technical assistance depending upon its outside value. Some forms of technical
assistance may be highly specialized, reducing abatement costs without providing inputs that could
be used for other purposes. For example, an importing country may provide assistance in the design,
construction, or operation of a fumigation facility in a exporting country's port for cargo destined
for its borders that has little value in other sectors in the country of origin. Alternatively, technical
assistance may be unspecialized, having value in the exporting country outside of the export sector.
An example might be training in entomology, pest control, or best management practices that could
also be useful in non-exported agricultural production.
We provide a possible explanation for existing technical assistance programs such as those men-
tioned above. We focus attention on cases for which technical assistance is so costly that it is not
efficient for the importer to provide it if there were symmetric information regarding risk abatement
costs. Even in such cases, it is optimal for the importer to provide technical assistance if this infor-
mation is in fact privately held by the exporter. We also find that the difference in outside value of
technical assistance to other sectors in the exporting country can have an important effect on the
qualitative characteristics of an optimal border protection policy. If technical assistance has no out-
side value, it is optimal for the regulator to offer exporters a choice of contracts in which a relatively
low tariff is paired with a relatively high penalty if caught with an invasive. If technical assistance
is fungible, however, it introduces countervailing incentives that make it optimal for the regulator
to use a one-size-fits-all policy involving a single tariff/penalty combination for all exporters.
Section 2 describes the basic model. Sections 3 and 4 respectively characterize the optimal policy
for specialized and unspecialized technical assistance. Section 5 concludes.
4
-------
1 Model
We consider a fixed population (normalized to one) of exporters each of whom makes a single
shipment.3 Each exporter is small enough that he considers equilibrium prices to be exogenous to
his own actions. For convenience, we assume transport costs are zero and exporters have an identical
opportunity cost (normalized to zero) of providing the good. They are differentiated only by an
abatement cost parameter 0 G 0 = (0,1], which we refer to as an exporter's type. The regulator
and exporters share common beliefs regarding the probability distribution of types, G(9), with
An exporter's cargo is either infected with invasive species or not, with a probability of infection
q. Exporters can undertake unobservable (to the regulator) abatement effort, e(9) > 0 to reduce q
below its baseline level, q < 1. Abatement effort has a type-dependent constant marginal cost of
0. The regulator may provide a technical assistance grant to all exporters. We assume that the
grant is a payment-in-kind perfectly substituting abatement effort such that an exporter's risk of
infection function is q(e{0) + (p^j with q' < 0, q" > 0, lim^oo q(z) > 0. The constant marginal cost
to the regulator of providing technical assistance is normalized to the average cost of effort over all
possible exporters, 0 = J* 0dG(0).4
If an infected shipment enters the importer's market undetected it causes damage S. The import-
ing country's border protection agency, referred to as the regulator, can conduct a costly imperfect
border inspection. The probability of revealing an invasive (if present) is r(I) G [0,1), where I is the
inspection intensity and r(0) = 0,r' > 0, lim/^o r'(I) = an(i r" < 0. The constant marginal cost
of inspection intensity is k.
Once discovered by the regulator, an infected good is destroyed. If all exporters ship their cargo,
inverse demand curve, with P' < 0 and liniM^o P(M) < S.
The regulator can levy a tariff r on all goods (regardless of inspection outcome), and, as in
Merel and Carter (2008) impose a penalty t on goods revealed to be infected. In practice, a border
protection agency is unlikely to have latitude to impose import tariffs at its discretion. The analysis
remains fundamentally unchanged, however, if r is given the interpretation of a service that is costly
3An important difference between our model and the previous literature is our implicit assumption of barriers to
entry. McAusland and Costello (2004) and Merel and Carter (2008) assume perfect competition with free entry and a
corresponding zero profit condition. Such a framework does not allow for an equilibrium with heterogeneous exporters
since those with low-costs would drive their competitors out of the market.
4As shown below, these assumptions ensure that under symmetric information it is optimal for the government
to provide no technical assistance.
5 We allow for the possibility that the regulator may design a policy such that some potential exporters may not
wish to ship their cargo.
d G{0) = g{0) d6.
imports
denotes the importing country's
5
-------
for the regulator to provide, but valuable for the exporter. For example, the regulator may be able
to devote resources to cover part of the cost of pre-clearance efforts in which domestic inspectors are
sent overseas (such as exists for Canadian and U.S. imports of tulip bulbs from the Netherlands)
or other measures (such as increased staffing of "fast lanes") designed to reduce inspection waiting
times.6 However, for expositional ease, and consistency with the preceding literature, we preserve
the label of r as an import tariff.
The penalty may take the form of a bond requirement that exporters would forfeit if an invasive
were found. Alternatively, it could be interpreted as a stylized depiction of expenditures the exporter
must incur to regain access to the importer's market after an invasive has been found. Mexico, for
example, has required that Canadian seed potato exporters discovered to have potato cyst nematodes
demonstrate they are cyst free before new shipments are allowed.
We assume I and are endogenously set by the regulator at a uniform level for all exporters.
The regulator can, however, offer a menu of options over which t and r can vary, effectively allowing
exporters to trade off a lower tariff for a higher penalty (or vice versa). Regulators are typically
constrained by trade agreements (e.g., membership in the World Trade Organization) that limit
their ability to use phytosanitary measures as a barrier to trade. To reflect this fact, we impose
a participation constraint; all exporters must earn weakly positive expected profit by sending a
shipment to the importing country.
We model the interaction between the regulator and exporters (all parties risk neutral) as a
non-repeated Stackelberg game in which the regulator is the first mover. The timing of the game
is as follows. The regulator first announces the inspection intensity and technical assistance grant,
then "assigns" a contract to each type exporter consisting of a tariff-penalty pair (r(6>),t(6>)}.7 We
refer to a contract assigned to an exporter of cost type 0 as a type 0 contract. Then exporters learn
their type and choose their contract. Finally, goods are exported, inspected, and monetary transfers
take place. We derive the optimal regulatory policy through backwards induction. We identify the
exporters' best response to any set of policy instruments proposed by the regulator, then use this
information to derive the regulator's optimal set of policy instruments.
For ease of exposition, we assume satisfaction of all second-order conditions for a unique optimum.
We also assume that the problem satisfies potential separation (Jullien, 2000), ensuring that a partial
pooling equilibrium does not arise simply due to the shape of the distribution function G(9).8
6 If the regulator's cost of expediting inspections by a unit of time is r, and is equal to the value of time to the
exporter, then even the notation goes through unaltered.
7The contract "assignment" refers to the contract that the regulator wishes each type of exporter to choose.
8Specifically, we require d\G(9)/g(9)\/d9 and d[[G(6>) — l]/g(6>)]/d6> > G(9)/g(9)9. See Bagnoli and Bergstrom
(2005) for properties of likelihood ratios for many common distribution functions. For details regarding solution
6
-------
2 Specialized technical assistance
In this section, we consider technical assistance with no value to other sectors of the exporting
country. For example, this might be provision of a highly specialized piece of equipment used for
detection of an invasive on a particular export crop.
For any given contract terms (r(6>), t(6>)}, an exporter of cost type 0 chooses abatement effort to
maximize profit, solving
(1) max P — rq(e + 4>)[P + t(9)] — t{6) — Oe.
e
The first-order conditions for (1) are
(2) -rq'(e + 4>)[P + t(d)]-d < 0
(3) e[rq'(e + 4>)[P + t(d)]+d] = 0.
For positive levels of effort, de/d = —1; increasing technical assistance offsets exporter effort
without reducing risk. Only if there is a corner solution with zero effort will a marginal increase in
technical assistance reduce overall risk.
Exporter expected profit from choosing his assigned contract is
(4) tt(6)) = P-rq e{6) + 4> [P +1(0)\ - t{9) - 6e{6).
The regulator seeks to maximize the importing country's consumer surplus, less damage caused by
invasives and net transfers abroad:
(5) max „M P(z)dz — ^ \P - rq(e(0) + (p)[P + t(0)\ - t(0) + q(e(0) + (p)[l - r\s\dG(0)
t{6),,
subject to the no protectionism constraint tt(0) > 0. Using Eq. (4), this expression simplifies to
(6) max [ P(z)dz— [ \q(e(6) + )[l — r]5 + 6e(6) — 7r(0)ldG(0) — kl — 9(f),
t(9),0,I,-k(9) J0 J0 I J
subject to 7t(0) > 0.
algorithms if potential separation does not hold, see Guesnerie and Laffont (1984).
7
-------
2.1 Benchmark (commonly known risk abatement cost types)
As a benchmark, suppose the regulator can observe and make contracts contingent upon cost
type. Since transfers are costly, she reduces t(9) as far as possible, leaving all exporters with zero
expected profit. Let t*(9),I*, and * denote the optimal contract values of the penalty, inspection
intensity and technical assistance, and e*(9) be the effort induced by the optimal contract. Using
pointwise optimization, the first order conditions for t*(9) are9
(7) —q'(e*(9) + (p)[r(I*)P + [1 — r(I*)]S\ — 9 < 0
(8) e*(9)[-q'(e(9) + 4>)[r(I*)P+[l-r(I*)}S\-9} = 0.
Combined with the first order condition for (1) this condition implies
(9) e*(0) [[1 - r(I*)]S - r(I*)t*(0)\ = 0.
This result is a straightforward manifestation of the equimarginal principle. For an interior solution,
the optimal penalty t* = [1 — r(I*)]S/r(I*) is chosen such that each exporter's marginal benefit
of effort, the reduction in expected fees r(I*)t*, is equated to the regulator's marginal benefit, the
reduction in expected damage [1 — r(I*)]6.
Consequently t*'(0) = 0 and Eq. (2) implies de(0)/A9 < 0. Let eg (9) denote the optimally induced
effort if there were no technical assistance. Since effort is non-increasing in 9 there is at most one
threshold type #*() = inf{6> : = (9)} below which eg(9) exceeds actual technical assistance, and
above which technical assistance exceeds eg(0). The assumptions on *) [r(I*)P + [1 -r(I*)]S] -9 AG(9) < 0
e*(0*)
l
-q'(*)[r(I*)P+ [1 -r(I*)]S] -9 AG(9) = 0.
h(*
Intuitively, the benefit to the regulator of a marginal increase in technical assistance varies by
exporter cost type. For types below the threshold, technical assistance merely offsets exporter effort.
Therefore there is no benefit in terms of risk reduction for these types. There is, however, a monetary
benefit inasmuch as the regulator can increase the tariff by the value of the reduced effort. The
9Recall that M = fg |^1 — q(e(0) + dG(0), so that by Liebniz' rule, d/dt j^/QM P(.z)d.zJ =
P(M) fg —q'(e(6) + )r(I)de/dt&G(0).
8
-------
sum of this marginal benefit is ^ ^ •* 9dG(9). For types above the threshold, the opposite is true.
Increasing technical assistance reduces risk, for a marginal benefit of { — I'i'P*) r(I*)P +
[1 — r(I*)]S }dG(6>), but does not have a direct monetary benefit. Since the penalty is optimally
set to ensure that the marginal benefit of risk reduction equals its marginal cost for all types, this
additional risk reduction is inefficient. Recalling that 9 = ^ 9dG(9), and using Eq. (2) implies that
condition (10) can be restated as
l
(12) - q'(*)r(I*) P + t(Q) -9 dG(9) < 0.
e*(0*)
The first order conditions for the optimal penalty (7) and (8) ensure that this expression is a strict
inequality for all * > 0. Consequently * = 0, and all exporters supply strictly positive effort.
The optimal inspection rate is chosen simultaneously with t*(0) to solve10
l
(13) r'(I*)q[6 - P]dG(9) - k = 0.
o
The expected marginal benefit from avoided net damage is set equal to the marginal inspection
cost.11
In addition to setting the stage for analysis with private information, this benchmark case serves
to highlight the implications of differences between our modeling framework and that of McAusland
and Costello (2004) and Merel and Carter (2008). Regarding the optimal values of the penalty
variable, t, and inspection intensity, /, our results are identical to those of Merel and Carter (2008).
The main difference is with respect to the optimal tariff. The free entry assumption in previous work
implies that the only benefit of a tariff is to restrict trade (and its associated costs). In our framework,
tariffs do not restrict trade, but only serve to transfer rents from exporters to the regulator. Our
optimal tariff (unlike the optimal penalty) is therefore different for each type of exporter.
2.2 Privately known risk abatement cost types
We now consider the case of both cost type and effort being privately known by the exporter.
For a contract allocation to be feasible, exporters must maximize profit by choosing their assigned
contract. With a slight abuse of notation, let e(9, 9) denote the effort provided by an exporter of
10Recall that M = fg |\ — q(e{6) + dG(d), so that by Liebniz' rule, d/dl j^/QM P(.z)d.zJ =
P(M) -q(e(d) + )r'(I)dG(e).
11 It is not necessarily optimal for the regulator to set the penalty arbitrarily high in order to eliminate inspection
costs; since q is strictly positive it may still be optimal to inspect even as abatement effort approaches infinity.
9
-------
type 9 with a contract of type 9. This requirement implies the following incentive compatibility
constraints:
(14) 9 £ argmax P — rq(e(9, 9) + ) [P +1(0)\ — t(9) — 9e(9, 9) for all (9, 9).
e
Using (2), the first order condition of the maximization problem in (14) is
(15) —rq(e(9) + )
(16) Sfwr
Consequently, incentive compatibility requires
(17) t'{9) < 0.
That is, the penalty must be non-increasing in type.
Differentiating (4) and using (15) implies that equilibrium profit is non-increasing in type at rate
(18) tt'(9) = —e(9).
Let eo (9) denote the effort induced by an optimal contract under asymmetric information with no
technical assistance. The regulator could eliminate the hidden information problem altogether by
setting 4> = maxe{eo(6>)}, i.e., providing so much technical assistance that no exporter provides any
effort. Since technical assistance is costly, however, such a strategy is generally not optimal.
Since the regulator's welfare function is decreasing in profit, it is optimal for the regulator to
select t(1) to leave the highest type with zero profit. Using (18), exporter profit can then be expressed
l
(19) tt(0) = e(z)dz.
10
-------
Incorporating participation and incentive compatibility constraints the regulator's problem is
M
(20) max P(z)dz — ^ q(e{9) + )[1 — r\S +
o o
After integrating by parts, this expression simplifies to
M
(21) max P(z)dz — ^ q(e(9) + )[l — r\S + e(9)
m,i,4> o o
The first-order conditions for t(9) are
+ e(z)dz } dG(0) - kl - i
G(9)
m j
dG(0) -kl -1
(22)
(23)
e(0)
—q'(e(9) + (f>)[rP + [1 — r]J] —9 <
G(9)~
-q'(e(9) + )[rP + [1 - r]c5] - 9-
9{9) J
G(9)
9(9)
0.
The right hand side (RHS) of (22) indicates the distortion induced by asymmetric information. Using
(2), Eq. (23) simplifies to
(24)
e(9)
—q'(e(9) + )[[! — r\5 — rt] —
G{9)
9(9)
0.
For a given inspection rate, the interior solution equilibrium value of the penalty is lower than the
benchmark case for all but the lowest type. Also, unlike the benchmark case, the penalty is decreasing
(rather than constant) in type.
Eq. (2) then implies de(9)/d9 < 0. Since effort is non-increasing in 9 there is at most one threshold
type 6(4>) = inf{6> : = eo(9)}. Similarly to the case without private information, the assumptions
on )[rP+[l-r}S\ dG{9) - 9 < 0
9(9) J g(0)
G(9) 1
4> -^d G(9)+ {-q'(4>)[rP+[l-r]S\-9}dG(9)
o 9\V) 0(0)
0.
Unlike in the benchmark case, technical assistance has two marginal benefits with respect to types
below the threshold As before, the effective subsidy causes exporters to reduce their effort,
allowing the regulator to increase the tariff by 9. In addition, this reduction in effort further reduces
payments to firms caused by the information asymmetry by G(9)/g(9). With respect to types above
11
-------
the threshold the marginal benefits of technical assistance are to reduce the risk of infection. With
private information, it is optimal for the regulator to set > 0. To see this note that, in contrast to
the benchmark case, the left hand side of (25) is strictly positive if there is no technical assistance,
i.e., the highest type is the threshold.
Using, Eq. (22), the first order condition for I is
i.e., the same expression (up to e(9) and ) as in the benchmark case. The distortion in inspection
intensity caused by private information is felt only indirectly through the effect on penalties and
technical assistance. The fact that penalties (and hence induced effort) are lower than under the
benchmark case places an upward distortion on inspection rates. This effect may be counterbalanced
by technical assistance. If the increase in abatement caused by technical assistance for 0 > 9()
results in a higher total abatement for these types than in the benchmark case it will place downward
pressure on inspection rates.
3 Unspecialized technical assistance
We now consider the possibility that technical assistance has a value to producers in other
sectors of the exporter's country. We assume that this outside value is positively correlated with the
exporter's cost type. For example, if entomological expertise is relatively valuable to an exporter in
a particular country it may also be relatively valuable to other producers in the same country, such
as farmers of a crop for domestic consumption. In this case, technical assistance can be thought of
as a lump sum transfer whose value is a function of an exporter's type. For simplicity, we assume
that this outside value is 94>.
In this case, the exporter's effort level solves
l
(27)
{r'(I)q(e(d) + 4>)[S-P]-k}dG(d) = 0,
0
(28)
max P — rq(e)[P + t(Q)\ — t(0) — 0[e — ],
e
and is not a function of technical assistance. The first-order conditions for (28) are
(30)
(29)
-q'{e)r[P + t{0)\ < 6
e —q'(e)r[P + t(0)\ — 0 = 0
12
-------
Equilibrium exporter expected profit is
(31) 7T(0) = P - rq(e(0))[P + t(0)] - t{0) - 0[e{0) - ].
The regulator seeks to maximize the importing country's consumer surplus, less damage caused
by invasives and net transfers abroad:
M 1
(32) max P(z)dz - {q(e(0))[l - r}5 + 0e(0) - n(0)} dG(0) - kl - 0.
t(e),i,4> o o
3.1 Commonly known risk abatement cost types
Recall from Section 2.1 that if technical assistance has no outside value, it can potentially increase
the amount of abatement undertaken by some exporters. In that case, it was not optimal for the
regulator to provide assistance if cost types were commonly known. If it has an outside value,
however, we have just shown that it does not affect the abatement of any exporter. Thus, the
benefit to the regulator of providing it is even lower. Consequently, the regulator has no incentive
to provide technical assistance with an outside value if exporter type is commonly known.
3.2 Privately known risk abatement cost types
If type is privately known, a feasible contract must satisfy incentive compatibility. Since trade is
voluntary, exporters only send shipments if their expected profit is positive. For a contract allocation
to be feasible, exporters must maximize profit by choosing their assigned contract. This requirement
implies the following incentive compatibility constraints:
(33) 0 G argmax P — rq(e(0, 0))[P +1(0)\ — t(0) — 0[e(0, 0) — \ for all (0, 0);
e
Using the same steps as Eqs. (15)-(18), it can be shown that incentive compatibility requires that the
penalty be non-increasing in type (i.e., satisfies condition (17)), and that equilibrium profit change
in type at rate
(34) ¦n'{0)=4>-e{0).
In contrast to the case for specialized technical assistance, profit is increasing in type if the exporter's
effort is less than the level of technical assistance. Intuitively, exporters face countervailing incentives
as in Lewis and Sappington (1989). One incentive is as before; exporters have an underlying incentive
13
-------
to overstate type to obtain higher compensation for their cost of effort. Exporters also face an
incentive to understate type, however. Doing so understates the value of the technical assistance
received. With specialized technical assistance, the former incentive dominates the latter for all
types. If technical assistance is unspecialized, however, its outside value makes it even more valuable
for high cost types. For those types with technical assistance "left over," i.e., whose effort is less
than , the latter incentive dominates.
For those exporters whose effort exactly equals the technical assistance, the two incentives cancel
out. Since e(9) is non-increasing in type, n(9) is convex.12 The regulator's welfare function is de-
creasing in profit. Consequently, the best she can do is reduce the profit of this last set (if it exists)
to zero. Condition (2) implies that effort is decreasing in 9 and increasing in t. Combined with (17),
a further implication is that the set of types receiving zero profit in equilibrium is a singleton.13
That is to say, maintaining a constant level of effort across an interval of types would require the
penalty to be increasing in type, which would violate incentive compatibility condition (17). Let
0° (), denote the zero profit type, and t° denote the penalty assigned to 9°. Using (34), exporter
profit can then be expressed:
°W{e(z) -4>}dz for 9 < 9°( — e(z)}dz for 9°(4>) < 9.
After incorporating participation and incentive compatibility constraints and integrating by
parts, the regulator's problem is
M 1
(36) max P(z)dz — {q(e(9))\\ — r\S + 9e(9)}dG(9) — kl
m, t° for 9 < 9°
(38) t° > t(9) for 9 > 9°.
12 As Lewis and Sappington (1989) provide an in-depth formal analysis of a problem with similar structure, here we
only provide a sketch of the proofs required to characterize the equilibrium contract. For a treatment of more general
classes of problems exhibiting countervailing incentives, see Maggi and Rodriguez-Clare (1995) and Jullien (2000).
13 If profit is either increasing or decreasing over the entire support, then it is optimal for one of the extreme types
to receive zero surplus.
14
-------
Let A(9) and /i(9) be Lagrange multipliers for (37) and (38). The first-order conditions for t(9) are
(40)
(39)
q'(e(9))[rP+[l-r}5\ -9
q'(e(9))[rP+[l-r}S}-9-® ^ + X(9) =0 for 9 < 9°()
(9))[rP + [l - r}5] - 9 - G{d^ ~ 1 ^ - p(9) =0 for 9 > 9°
It is straightforward to show (see Lewis and Sappington, 1989, Lemma 5) that if 9°() G (0,1) then
there will be one and only one pooling interval over which the penalty is constant. Moreover, that
interval contains 9°(), and the pooling penalty is optimally set to to = [1 — r]S/r. Note that this
amount is the same as under no adverse selection (conditional on I).
Intuitively, whenever constraints (37) and (38) do not bind, the Potential Separation assumption
ensures that the paths for t(9) as defined by Eqs. (39) and (40) are strictly decreasing. Thus there
can be no pooling interval that does not contain 9°().
Let t°(9) denote the penalty path defined by Eq. (39), setting A(9) = 0. Note that on that path,
Similarly, let ta 1(6>) denote the penalty path defined by Eq. (40), with /i,(9) set to zero. Note that
in this case
Since q"de/dt > 0, for any given 9, it follows that t°(9) < ta^1(9). Thus, if there is no pooling (both
Lagrange multipliers are zero) then the value of ta(9) as 9 approaches 9°(4>) from below is strictly
lower than the limit of ta^1(9) as 9 approaches 9°(4>) from above. Such a result, however would
violate the monotonicity condition t'(9) < 0. Thus, the two constraints must bind (i.e., there is
pooling, and the Lagrange multipliers are non-zero) for some non-degenerate interval around 9°().
Gathering these results, and letting 9a() and 9l3() denote the lower and upper bounds of the
pooling interval, we have
(41)
q'(e(9))[rP+[l-r]S\-9=^ > 0.
g{y)
(42)
q\e{9))[rP + [1 - r]S\ - 9 = G{0) 1 < 0.
9W
n i
ta^ _ gje)e_ for Q <
(43)
t(9) = t° = for 9a{4>) <9 < 9'3(4>)
15
-------
6
o e °{ since
lini0^oiG($) < t° and tG_1(l) = t°, and the potential separation property requires that both ta
and tG_1 be non-increasing in 9. Consequently, the regulator can do no better than offer the same
penalty, [1 — r(I)\6/r(I), to all exporters.
The optimal levels of and I are then obtained by solving
M 1
(44) max P(z)dz — {q(e(9))[l — r(I)]6 + 9e(9)}dG(9) — kl
is
e°(0) l
(45) G(0)dQ- [1 - G(Q)]dQ = 0.
0 0°(0)
By Eq. (34), a marginal increase in technical assistance alters the rate at which surplus profit changes
over type, reducing it (in absolute value) for 0 < 9°(4>) and increasing it for 0 > 9°(4>). The marginal
reduction in surplus payments for the former interval is ^ ^ G(9)d9 and the marginal increase for
16
-------
the latter is — G(Q)\dQ. Optimally, the regulator chooses such that the net marginal effect
is zero. Since 6°(0) = 1, the net marginal effect of increasing technical assistance from zero is strictly
positive, implying that in equilibrium > 0.
The first-order condition for I is
l e°(0) l
r'(I)q(e(d)+4>)[S-P}dG(d)-k = G(0)ffr'(I)dd- [1 - G(0)]fr'(I)dd
0 0 0°(0)
(46) = (0) ^X^de - [1-G(e)k,(e(e))r,(/)d6)
V ' Q r{I)q"{e{9)) ^ r{I)q"{e{9))
Notice that in contrast with Eqs. (13) and (27), asymmetric information introduces a distortion
in the optimal inspection level, indicated by the right hand side of Eq. (46). With commonly held
information it is optimal to have a uniform penalty for all exporters. In the case in which technical
assistance has no outside value, private information introduces a distortion, making it optimal to
vary the penalty by exporter type. The optimal inspection rate is not directly distorted, however.
If technical assistance has an outside value, the situation is reversed. The countervailing incentive
provided by the technical assistance grant creates a pooling equilibrium in which it is not optimal
to vary penalties by exporter. The optimal inspection intensity is distorted since it affects the type
that receives zero surplus and hence the accumulated surplus over the whole support. Whether it is
distorted upwards or downwards depends upon the distribution of exporter types.
4 Conclusion
Implementation of border control measures to reduce the risk of unintentional entry of invasive
species is likely to be affected by both hidden actions and private information. Hidden actions occur
if exporters can undertake unobservable (to the importing country's border protection agency) effort
to reduce the risk of an invasive being on their shipment. Private information exists if exporters are
heterogeneous in their cost of undertaking such actions.
In this paper we have characterized an optimal border control strategy under such conditions.
The border control strategy consists of an inspection intensity, a penalty levied if inspections reveal
the presence of an invasive, technical assistance provided by the regulator, and a transfer.
The transfer is not necessarily an import tariff, and can be interpreted as other types of existing
policies that are more likely to be under the discretion of a regulating agency, such as pre-clearance
inspections. Dating from 1951, the oldest North American pre-clearance program involves inspectors
being sent to the Netherlands to prevent importation of pests on plant bulbs. The program benefits
17
-------
Dutch exporters by reducing inspection time and lost product (rejected bulbs can be used in another
market). This program involves coordination between the Dutch government, exporters, and U.S.
and Canadian inspectors.
We model inspection intensity and technical assistance as being applied equally to all exporters.
We also consider a policy innovation that would allow exporters to voluntarily reduce their import
tariff in exchange for an increased penalty to be levied in the event that an invasive is found in their
shipment.
We consider this set of policy tools under two settings regarding technical assistance relevant
to real world agricultural trade in North America. In the first, technical assistance takes the form
of a highly specialized type of training or equipment that has no value outside the exporting firm,
such as pest control for a specific grower's location only. Under the second, technical assistance does
have an outside value that is correlated with the exporter's risk abatement cost. We compare these
outcomes to a benchmark case in which there is no private information.
Without private information, there is need for neither technical assistance nor variation in tariffs
and penalties. The penalty is set at a level sufficient to induce the optimal level of risk abatement
effort. It is similar to a Pigouvian tax in that producers choose abatement such that their marginal
cost is equated to the expected penalty. At the optimum, the regulator sets the penalty equal to
expected marginal benefit of abatement so that in equilibrium the equimarginal principle is satisfied
and the expected marginal costs are equal across firms and equal expected marginal benefit.
With private information, the problem becomes more complicated. In the absence of technical
assistance firms have an underlying incentive to behave in a manner that overstates abatement
costs. Doing so limits the maximum tariff that the regulator is willing to impose. The best that the
regulator can do is to allow exporters to select a tariff/penalty combination from a menu of options.
Such a strategy sacrifices economic efficiency (arising from violation of the equimarginal principal)
in exchange for a reduction in information rents paid to exporters. In contrast to cases examined
in previous literature in which both the regulator and exporter are equally informed, we find that
asymmetric information provides a strong incentive for the regulator to provide positive levels of
technical assistance. This result may help explain the existence of policies such as the Clean Stock
program and importer financed support for treatment to meet ISPM #15.
We find that the outside value of technical assistance crucially affects the optimal regulatory
structure. If technical assistance is highly specialized, it is in the regulator's interest to provide
a strictly positive amount. Technical assistance helps the regulator since its value to firms is an
increasing function of abatement costs. Intuitively, if firms claim to have high abatement costs, they
18
-------
are also claiming that the technical assistance is valuable to them. The higher the value of the
technical assistance, the higher the tariff that the regulator can levy and still have the exporter be
willing to ship the good.
If technical assistance is unspecialized, the problem is more complicated, but the solution is
simpler. Without an outside value, the upper bound of the value of technical assistance to the
exporter is the amount of effort that it displaces. If it has an outside value, this is no longer the
case. Even if a firm undertakes no effort, it can resell the technical assistance in its home market. In
practice, this distinction is important since it introduces the potential for countervailing incentives.
Very low-cost exporters have high levels of abatement and use all their technical assistance. Since
it has a low value, however, their dominant incentive is to overstate their true cost to get a lower
tariff. At the opposite extreme, very high-cost exporters have low levels of abatement, but receive a
relatively large income from reselling technical assistance. Consequently, their dominant incentive is
to understate their true cost to get a lower tariff. For some intermediate type these two incentives
can exactly counteract each other, leaving them with no incentive pulling in either direction. We
show that under these conditions the optimal policy exhibits pooling over the entire range of types:
they all have the same penalty and tariff. Qualitatively, the policy resembles that under conditions
without private information except that there is strictly positive provision of technical assistance.
In practice, it would be simpler to administer than if technical assistance were specialized and may
yield higher expected welfare for the regulator. It also has the possible advantage of being non-
discriminatory with respect to trading partners. Perhaps counter-intuitively, in some circumstances
it may be in the regulator's interest to provide technical assistance in a manner that the recipient
can resell it.
References
Bagnoli, M. and Bergstrom, T. (2005). Log-concave probability and its applications. Economic The-
ory 26: 445-469.
Batabyal, A. A. and Beladi, H. (2009). Trade, the damage from alien species, and the effects of
protectionism under alternate market structures. Journal of Economic Behavior and Organization
70: 389-401.
Buhle, E. R., Margolis, M. and Ruesink, J. L. (2005). Bang for buck: cost-effective control of invasive
species with different life histories. Ecological Economics 52: 355-366.
19
-------
Burnett, K. M., D'Evelyn, S., Kaiser, B. A., Nantamanasikarn, P. and Roumasset, J. A. (2008).
Beyond the lamppost: Optimal prevention and control of the brown tree snake in Hawaii. Ecological
Economics 67: 66-74.
Costello, C. and McCausland, C. (2003). Protectionism, trade and measures of damage from exotic
species introductions. American Journal of Agricultural Economics 85: 964-975.
Costello, C., Springborn, M., McAusland, C. and Solow, A. (2007). Unintended biological invasions:
Does risk vary by trading partner? Journal of Environmental Economics and Management 54:
262-276.
Eiswerth, M. and Johnson, W. (2002). Managing nonindigenous invasive species: Insights from dy-
namic analysis. Environmental and Resource Economics 23: 319-342.
Gramig, B., Horan, R. and Wolf, C. (2009). Livestock disease indemnity design when moral hazard
is followed by adverse selection. American Journal of Agricultural Economics 91: 627-641.
Guesnerie, R. and Laffont, J.-J. (1984). A complete solution to a class of principal-agent problems
with an application to the control of a self-managed firm. Journal of Public Economics 25: 329-369.
Horan, R. D. and Lupi, F. (2005). Economic incentives for controlling trade-related biological inva-
sions in the Great Lakes. Agricultural and Resource Economics Review 34: 75-89.
Jullien, B. (2000). Participation constraints in adverse selection models. Journal of Economic Theory
93: 1-47.
Kim, C., Lubowski, R., Lewandrowski, J. and Eiswerth, M. (2006). Prevention or control: Optimal
government policies for invasive management. Agricultural and Resource Economics Review 35:
29-40.
Lewis, T. and Sappington, D. (1989). Countervailing incentives in agency problems. Journal of
Economic Theory 49: 294-313.
Maggi, G. and Rodriguez-Clare, A. (1995). On countervailing incentives. Journal of Economic Theory
66: 238-263.
McAusland, C. and Costello, C. (2004). Avoiding invasives: Trade-related policies for controlling
unintentional exotic species introductions. Journal of Environmental Economics and Management
48: 954-977.
20
-------
Merel, P. R. and Carter, C. A. (2008). A second look at managing import risk from invasive species.
Journal of Environmental Economics and Management 56: 286-290.
Olson, L. and Roy, S. (2002). Economics of controlling a stochastic biological invasion. American
Journal of Agricultural Economics 84: 1311-1316.
Olson, L. and Roy, S. (2005). On prevention and control of an uncertain biological invasion. Review
of Agricultural Economics 27: 491-497.
Sheriff, G. and Osgood, D. (2010). Disease forecasts and livestock health disclosure: A shepherd's
dilemma. American Journal of Agricultural Economics : doi:10.1093/ajae/aap042.
Shogren, J. (2000). Risk reduction strategies against the 'explosive invader'. In Perrings, C.,
Williamson, M. and Dalmazzone, S. (eds), The Economics of Biological Invasions. Elgar Ltd.
Starbird, S. A. (2005). Moral hazard, inspection policy, and food safety. American Journal of Agri-
cultural Economics 87: 15-27.
21
------- |